I'm so sorry to hear about your teacup! I have the same glass cup from Adagio and I know I would be crushed if something happened to it. I hope you get a new one soon!
Heh, I pretty much do what Abx, does... I just rinse my teaware out with water and dry it with a towel or let it dry itself (depending on how lazy I am that day).
I figure the only thing that is going into it is tea (i.e. flavored water) so why bother using soap.